Question: Solve for $x$. Enter the solutions from least to greatest. $4x^2 + 40x + 84 = 0$ $\text{lesser }x = $
Answer: $\begin{aligned} 4x^2 + 40x + 84 &= 0 \\\\ 4(x^2+10x+21)&=0 \end{aligned}$ Now let's factor the expression in the parentheses. $x^2+10x+21$ can be factored as $(x+7)(x+3)$. $\begin{aligned} 4(x+7)(x+3)&=0 \\\\ x+7=0&\text{ or }x+3=0 \\\\ x=-7&\text{ or }x=-3 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= -7 \\\\ \text{greater }x &= -3 \end{aligned}$